Structures · Algebra
HasEnoughRootsOfUnity
This is a type class recording that a commutative monoid M contains primitive nth
roots of unity and such that the group of nth roots of unity is cyclic.
Such monoids are suitable targets in the context of duality statements for groups
of exponent n.
- Shape
- 2 explicit arguments · adds prim, cyc
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by0
Nothing extends this class yet.
Concrete types that are instances4
- ZMod
- AlgebraicClosure
- Circle
- SeparableClosure
How is a type an instance?
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Assumed by63
- CommGroup.subgroupOrderIsoSubgroupMonoidHom
- IsCyclotomicExtension.Rat.subgroupGalEquivSubgroupChar
- MulChar.subgroupOrderIsoSubgroupMulChar
- HasEnoughRootsOfUnity.of_dvd
- HasEnoughRootsOfUnity.natCard_rootsOfUnity
- CommGroup.monoidHomMonoidHomEquiv
- HasEnoughRootsOfUnity.exists_primitiveRoot
- IsCyclotomicExtension.Rat.intermediateFieldEquivSubgroupChar
- MulChar.mulCharEquiv
- MonoidHom.domRestrict_surjective
- modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_pow
- CommGroup.exists_apply_ne_one_of_hasEnoughRootsOfUnity
- CommGroup.card_domRestrictHom_ker
- CommGroup.monoidHomMonoidHomEquiv_symm_apply_apply
- HasEnoughRootsOfUnity.prim
- CommGroup.monoidHom_mulEquiv_of_hasEnoughRootsOfUnity
- CommGroup.card_monoidHom_of_hasEnoughRootsOfUnity
- cyclotomicCharacter.toZModPow_toFun
- MulChar.mulEquiv_units
- MulChar.exists_apply_ne_one_of_hasEnoughRootsOfUnity
- CommGroup.card_subgroupOrderIsoSubgroupMonoidHom
- MulChar.domRestrictHom_surjective
- DirichletCharacter.sum_characters_eq
- cyclotomicCharacter.toZModPow
- MulChar.mulCharEquiv_symm_apply_apply
- DirichletCharacter.card_eq_totient_of_hasEnoughRootsOfUnity
- CommGroup.forall_apply_eq_apply_iff
- DirichletCharacter.sum_char_inv_mul_char_eq
- cyclotomicCharacter.toFun_apply
- DirichletCharacter.sum_characters_eq_zero
- MulChar.card_subgroupOrderIsoSubgroupMulChar
- IsCyclotomicExtension.Rat.card_subgroupGalEquivSubgroupChar
- cyclotomicCharacter.toFun_spec
- IsCyclic.monoidHom_equiv_self
- DirichletCharacter.mulEquiv_units
- DirichletCharacter.exists_apply_ne_one_of_hasEnoughRootsOfUnity
- IsCyclotomicExtension.Rat.intermediateFieldEquivSubgroupChar.congr_simp
- instFiniteMonoidHomUnitsOfHasEnoughRootsOfUnityExponent
- MonoidHom.restrict_surjective
- CommGroup.apply_monoidHomMonoidHomEquiv
- IsCyclotomicExtension.Rat.mem_subgroupGalEquivSubgroupChar_iff
- CommGroup.card_restrictHom_ker
- MulChar.subgroupOrderIsoSubgroupMulChar.congr_simp
- HasEnoughRootsOfUnity.finite_rootsOfUnity
- MulChar.apply_mulCharEquiv
- IsCyclotomicExtension.Rat.mem_subgroupGalEquivSubgroupChar_symm_iff
- CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_iff
- MulChar.restrictHom_surjective
- MulEquiv.hasEnoughRootsOfUnity
- MulChar.card_eq_card_units_of_hasEnoughRootsOfUnity
Ancestors0
No ancestors.